Alright, here we go. If I want to turn this globe into a flat map, I'm going to have to cut it open. In order to get this globe to look anything close to a rectangle lying flat, I've had to cut it in several places. I've had to stretch it so that the countries are starting to look all wonky. And even still it's almost impossible to get it to lay flat. And that right there is the eternal dilemma of mapmakers. The surface of a sphere cannot be represented as a plane without some form of distortion. That was mathematically proved by this guy long time ago. Since around the 1500s, mathematicians have set about creating algorithms that would translate the globe into something flat. And to do this, they use a process called projection. Popular rectangular maps use a cylindrical projection. Imagine putting a theoretical cylinder over the globe and projecting each of the points of the sphere onto the cylinder's surface. Unroll the cylinder and you have a flat rectangular map. But you could also project the globe onto other objects. And the math used by mapmakers to project the globe will affect the way the map looks once it's all flattened out. And here's the big problem. Every one of these projections comes with tradeoffs in shape, distance, direction, and land area. Certain map projections can either be misleading or very helpful depending on what you're using them for. Here's an example. This map is called the Mercator projection. If you're American, you probably studied this map in school. It's also the projection that Google Maps uses. The Mercator projection is popular for a couple of reasons. First, it generally preserves the shape of countries. Brazil on the globe has the same shape as Brazil on the Mercator projection. But the original purpose of the Mercator projection was navigation. It preserves direction, which is a big deal if you're trying to navigate the ocean with only a compass. It was designed so that a line drawn between two points on the map would provide the exact angle to follow on a compass to travel between those two points. If we go back to the globe, you can see that this line is not the shortest route, but at least it provides a simple, reliable way to navigate across the ocean. Gerardus Mercator, who created the projection in the 16th century, was able to preserve direction by varying the distance between the latitude lines and also making them straight, creating a grid of right angles. But that created some other problems. Where the Mercator fails is its representation of size. Look at the size of Africa as compared to Greenland. On the Mercator map, they look about the same size. But if you look at a globe for Greenland's true size, you'll see that it's way smaller than Africa, by a factor of 14 in fact. If we put a bunch of dots onto the globe that are all the same size, and then project that onto the Mercator map, we will end up with this. The circles retain their round shape but are enlarged as they get closer to the poles. One modern critique of this is that the distortion perpetuates imperialist attitude of European domination over the Southern Hemisphere. The Mercator projection has fostered European imperialist attitudes for centuries and created an ethnic bias against the third world. Really? So if you want to see a map that more accurately displays land area, you can use the Gall-Peters projection. This is called an equal-area map. Look at Greenland and Africa now. The size comparison is accurate, much better than the Mercator. But it's obvious now that the country shapes are totally distorted. Here are those dots again so that we can see how the projection preserves area while totally distorting shape. Something happened in the late 60s that would change the whole purpose of mapping and the way that we think about projections. Satellites orbiting our planet started sending location and navigation data to little receiver units all around the world. Today, orbiting satellites of the Navy navigation satellite system provide round-the-clock, ultra-precise position fixes from space to units everywhere in any kind of weather. This global positioning system wiped out the need for paper maps as a means of navigating both the sea and the sky. Map projection choices became less about navigational imperatives and more about aesthetic, design, and presentation. The Mercator projection, that once-vital tool of pre-GPS navigation, was shunned by cartographers who now saw it as misleading. But even still, most web mapping tools like Google Maps use the Mercator. This is because the Mercator's ability to preserve shape and angles makes close-up views of cities more accurate. A 90-degree left turn on the map is a 90-degree left turn on the street that you're driving down. The distortion is minimal when you're close up. But on a world map scale, cartographers rarely use the Mercator. Most modern cartographers have settled on a variety of non-rectangular projections that split the difference between distorting either size or shape. In 1998, the National Geographic Society adopted the Winkel Tripel projection because of its pleasant balance between size and shape accuracy. But the fact remains that there's no right projection. Cartographers and mathematicians have created a huge library of available projections, each with a new perspective on the planet and each useful for a different task. The best way to see the Earth is to look at a globe. But as long as we use flat maps, we'll have to deal with the tradeoffs of projections. And just remember, there's no right answer. If you yourself want to poke fun at the Mercator projection, you can do so by going to thetruesize.com, which is a fun tool that allows you to drag around whatever country you want around the map and see how it is distorted depending on where it is. I also want to say a big thanks to Mike Bostock, whose open-source project on map projections was a huge help in this video. I'll put a link for both of those things down in the description.
A man holds a large, inflatable globe in a studio setting, explaining his intention to flatten it.
"If I want to turn this globe into a flat map, I'm going to have to cut it open."
Setting: photography studio — bright, even studio lighting
People (1):
• standing, wearing light blue button-down shirt and dark blue jeans, short brown hair hair — bearded, focused expression
Text: "Vox"
The man stabs the top of the inflatable globe with an orange-handled knife, causing it to deflate rapidly.
Setting: photography studio — bright studio lighting
People (1):
• bending over, wearing light blue button-down shirt and dark blue jeans, short brown hair hair — not visible
The man is kneeling on the floor, struggling to unfold and flatten the deflated globe, cutting it further with the knife.
"In order to get this globe to look anything close to a rectangle lying flat, I've had to cut it in several places."
Setting: photography studio — bright studio lighting
People (1):
• kneeling on the floor, wearing light blue button-down shirt and dark blue jeans, short brown hair hair — partially visible, concentrated
The man continues to try and flatten the globe, stepping on it and pulling it, but it remains wrinkled and uneven. The narrator begins to explain the core problem.
"And that right there is the eternal dilemma of mapmakers."
Setting: photography studio — bright studio lighting
People (1):
• kneeling over the globe, wearing light blue button-down shirt and dark blue jeans, short brown hair hair — not visible
A historical portrait of Carl Friedrich Gauss appears in an oval frame, surrounded by complex mathematical equations and diagrams related to spherical geometry.
"That was mathematically proved by this guy long time ago."
Setting: n/a (graphical overlay) — n/a (illustration)
People (1):
• seated portrait, wearing dark academic robe, graying, receding hair — serious, looking slightly to the side
Text: "Gauss' Theorema Egregium", "Carl Friedrich Gauss"
The man stands on the still-inflated globe, and the word 'Projection' appears over it with graphical elements.
"And to do this, they use a process called projection."
Setting: photography studio — bright studio light
People (1):
• standing on the globe and dark blue jeans — not visible (only legs)
Text: "Projection"
A man places a large white paper cylinder over the inflatable globe. Animated lines then project from the globe's surface outward onto the inside of the cylinder.
"Imagine putting a theoretical cylinder over the globe and projecting each of the points of the sphere onto the cylinder's surface."
Setting: photography studio — bright studio lighting
People (1):
• bending over, wearing light blue button-down shirt and dark blue jeans, short brown hair hair — not visible
The man unrolls a large sheet of white paper on the floor, revealing a black outline of a world map.
"Unroll the cylinder and you have a flat rectangular map."
Setting: photography studio — bright studio lighting
People (1):
• standing at the top of the map and dark blue jeans — not visible (only feet)
Text appears on screen over a rapidly changing background of many different distorted map projections.
"And here's the big problem."
Setting: n/a (graphic) — n/a (graphic)
Text: "Here's the BIG problem:"
A black silhouette of a Mercator projection map appears on a white background.
"This map is called the Mercator projection."
Setting: n/a (graphic) — n/a (graphic)
Text: "MERCATOR"
A screenshot of the Google Maps interface is shown, displaying the world with the Mercator projection.
"It's also the projection that Google Maps uses."
Setting: n/a (digital interface) — n/a (screenshot)
Text: "United States, Canada, Mexico, etc."
An animation shows the outline of South America next to a 3D globe. The outline of Brazil is extracted from the globe and shown to match the shape on the flat outline, highlighting its preservation of shape.
"Brazil on the globe has the same shape as Brazil on the Mercator projection."
Setting: n/a (animation) — n/a (animation)
A colorful animated Mercator map is shown. A line is drawn from northern South America to the UK. An inset shows an old drawing of a sailing ship on a navigational chart.
"It preserves direction, which is a big deal if you're trying to navigate the ocean with only a compass."
Setting: n/a (animation) — n/a (animation)
An animation shows the grid of a Mercator map, with red lines indicating the increasing distance between latitude lines as they move away from the equator.
"But that created some other problems. Where the Mercator fails is its representation of size."
Setting: n/a (animation) — n/a (animation)
On a black and white Mercator map, the landmasses of Greenland and Africa are highlighted and boxed, showing their similar apparent sizes.
"Look at the size of Africa as compared to Greenland. On the Mercator map, they look about the same size."
Setting: n/a (graphic) — n/a (graphic)
Text: "MERCATOR"
A side-by-side comparison. On the left, a realistic 3D globe shows Greenland is much smaller than Africa. On the right, an animation shows Greenland's landmass stretched to cover almost the entirety of Africa, illustrating the 14x size distortion.
"by a factor of 14 in fact."
Setting: n/a (animation) — n/a (animation)
Text: "REALITY", "MERCATOR"
An animation shows equally sized yellow circles on a globe being projected onto a flat Mercator map. The circles near the equator stay small, while the circles near the poles become massively enlarged.
"The circles retain their round shape but are enlarged as they get closer to the poles."
Setting: n/a (animation) — n/a (animation)
A clip from the TV show 'The West Wing' plays inside a frame on the Mercator map with yellow dots. A woman explains the political implications of the map's distortion.
"The Mercator projection has fostered European imperialist attitudes for centuries and created an ethnic bias against the third world. Really?"
Setting: An office or presentation room (in clip) — dim, indoor lighting (in clip)
People (1):
• standing, wearing tan blazer over a gray top, reddish-brown, shoulder-length hair — serious, speaking
A black silhouette of a Gall-Peters projection map appears. It is noticeably taller and more stretched vertically than the Mercator.
"So if you want to see a map that more accurately displays land area, you can use the Gall-Peters projection."
Setting: n/a (graphic) — n/a (graphic)
Text: "GALL-PETERS"
A side-by-side comparison of the Gall-Peters and Mercator projections, focusing on the relative sizes of Greenland and Africa on each.
"The size comparison is accurate, much better than the Mercator. But it's obvious now that the country shapes are totally distorted."
Setting: n/a (graphic) — n/a (graphic)
Text: "GALL-PETERS", "MERCATOR"
The yellow dot animation is shown on the Gall-Peters map. The dots all remain the same size (area) but are stretched into vertical ovals, especially near the equator and poles.
"Here are those dots again so that we can see how the projection preserves area while totally distorting shape."
Setting: n/a (animation) — n/a (animation)
Archival footage of a rocket launching, followed by an animation of a satellite orbiting the Earth and sending signals.
"Satellites orbiting our planet started sending location and navigation data to little receiver units all around the world."
Setting: space — n/a (animation)
Archival footage shows two men in uniform working at a drafting table, using tools to draw on a paper map.
"This global positioning system wiped out the need for paper maps as a means of navigating both the sea and the sky."
Setting: indoor military or technical setting — warm, slightly dim
People (1):
• standing at a table, wearing khaki uniforms, short dark hair hair — concentrated, looking down
An old, sepia-toned Mercator map is shown. It then appears to burn away from the edges, dissolving into a white background.
"The Mercator projection, that once-vital tool of pre-GPS navigation, was shunned by cartographers who now saw it as misleading."
Setting: n/a (animation) — n/a (animation)
A view of Google Maps zooms from a world view down to a country view (USA), and then into a close-up street-level view.
"This is because the Mercator's ability to preserve shape and angles makes close-up views of cities more accurate."
Setting: n/a (digital interface) — n/a (screen capture)
Text: "S 88th Ave, 103rd St"
A rapid montage of various modern, non-rectangular, black and white map projections flashes on the screen.
"Most modern cartographers have settled on a variety of non-rectangular projections that split the difference between distorting either size or shape."
Setting: n/a (animation) — n/a (animation)
A black and white map using the Winkel Tripel projection is shown. It has curved longitude lines and a rounded, less rectangular shape.
"In 1998, the National Geographic Society adopted the Winkel Tripel projection because of its pleasant balance between size and shape accuracy."
Setting: n/a (graphic) — n/a (graphic)
Text: "WINKEL TRIPEL"
A rapid montage of different map projections continues, emphasizing the variety and lack of a single correct answer.
"But the fact remains that there's no right projection."
Setting: n/a (animation) — n/a (animation)
The video cuts back to the man on the studio floor, still wrestling with the wrinkled, deflated globe, unable to make it perfectly flat.
"But as long as we use flat maps, we'll have to deal with the tradeoffs of projections. And just remember, there's no right answer."
Setting: photography studio — bright studio lighting
People (1):
• kneeling on the floor, wearing light blue button-down shirt and dark blue jeans, short brown hair hair — not visible
The narrator, Johnny Harris, appears in a close-up shot, speaking directly to the camera. The screen shows credits and a demonstration of thetruesize.com website.
"If you yourself want to poke fun at the Mercator projection, you can do so by going to thetruesize.com, which is a fun tool that allows you to drag around whatever country you want around the map and see how it is distorted depending on where it is."
Setting: indoor setting — soft, frontal lighting
People (1):
• head and shoulders shot, wearing gray knit sweater, short brown hair hair — bearded, speaking to camera
Text: "VIDEO BY JOHNNY HARRIS GINA BARTON ALVIN CHANG PHIL EDWARDS"
The narrator continues speaking to the camera while credits and a screen recording of Mike Bostock's project are displayed.
"I also want to say a big thanks to Mike Bostock, whose open-source project on map projections was a huge help in this video. I'll put a link for both of those things down in the description."
Setting: indoor setting — soft, frontal lighting
People (1):
• head and shoulders shot, wearing gray knit sweater, short brown hair hair — bearded, speaking to camera
Text: "SPECIAL THANKS STEPHEN SMITH MIKE BOSTOCK (PROJECTION TRANSITIONS) ALEX TAIT (NATIONAL GEOGRAPHIC) BOJAN SAVRIC"